Table of Contents
Geometry
Volume 2013, Article ID 484508, 8 pages
http://dx.doi.org/10.1155/2013/484508
Research Article

Fundamental Group and Covering Properties of Hyperbolic Surgery Manifolds

Dipartimento di Scienze Fisiche, Informatiche e Matematiche, Università di Modena e Reggio E., Via Campi 213/B, 41100 Modena, Italy

Received 10 June 2013; Accepted 27 August 2013

Academic Editor: Manuel Sanchis

Copyright © 2013 Alberto Cavicchioli et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We study a family of closed connected orientable 3-manifolds obtained by Dehn surgeries with rational coefficients along the oriented components of certain links. This family contains all the manifolds obtained by surgery along the (hyperbolic) 2-bridge knots. We find geometric presentations for the fundamental group of such manifolds and represent them as branched covering spaces. As a consequence, we prove that the surgery manifolds, arising from the hyperbolic 2-bridge knots, have Heegaard genus 2 and are 2-fold coverings of the 3-sphere branched over well-specified links.